16=48x-16x^2

Solution for 16=48x-16x^2 equation:

16=48x-16x^2

We move all terms to the left:

16-(48x-16x^2)=0

We get rid of parentheses

16x^2-48x+16=0

a = 16; b = -48; c = +16;
Δ = b2-4ac
Δ = -482-4·16·16
Δ = 1280
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1280}=\sqrt{256*5}=\sqrt{256}*\sqrt{5}=16\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-16\sqrt{5}}{2*16}=\frac{48-16\sqrt{5}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+16\sqrt{5}}{2*16}=\frac{48+16\sqrt{5}}{32}
$